We will use the abstract index notation, and the metric and its inverse to raise and lower indices as convenient.
Notice that since \(A\)  is an automorphism, the map \(W\)  in (REF ) is non-degenerate.
Appendix B in [1]} will be useful in the following.
Since \(M\)  is orientable, it has a volume 4-form \(\varepsilon _{abcd}\) , and
the metric allows to normalize it as \(\varepsilon ^{abcd}\varepsilon _{abcd}=(-1)^{s}4!\) .
